The present invention relates generally to systems and methods of processing synthetic aperture radar signals and, more particularly, relates to systems and methods of autofocusing synthetic aperture radar signals utilizing superresolution processing.
There has been a continuing effort to develop radar systems which are suitable for high-resolution applications, such as ground-mapping and air reconnaissance. Initially, this finer resolution was achieved by the application of pulse-compression techniques to conventional radar systems which were designed to achieve range resolution by the radiation of a short pulse, and angular, or azimuth, resolution by the radiation of a narrow beam. The pulse-compression techniques provided significant improvement in the range resolution of the conventional radar systems, but fine angular resolution by the radiation of a narrow beam still required a large-diameter antenna which was impractical to transport with any significant degree of mobility. Subsequent to the development of pulse-compression techniques, synthetic aperture radar (SAR) techniques were developed for improving the angular resolution of a radar system to a value significantly finer than that directly achievable with a radiated beam width from a conventional antenna of comparable diameter.
In prior techniques, an equivalent to a large-diameter antenna was established which was comprised of a physically long array of antennas, each having a relatively small diameter. In the case of a long antenna array, a number of radiating elements were positioned at sampling points along a straight line and transmission signals were simultaneously fed to each element of the array. The elements were interconnected such that simultaneously received signals were vectorially added to exploit the interference between the signals received by the various elements to provide an effective radiation pattern which was equivalent to the radiation pattern of a single element multiplied by an array factor. That is, the product of a single element radiation pattern and the array factor resulted in an effective antenna pattern having significantly sharper antenna pattern lobes than the antenna pattern of the single element.
SAR systems are based upon the synthesis of an effectively long antenna array by signal processing means rather than by the use of a physically long antenna array. With an SAR, it is possible to generate a synthetic antenna many times longer than any physically large antenna that could be conveniently transported. As a result, for an antenna of given physical dimensions, the SAR will have an effective antenna beam width that is many times narrower than the beam width which is attainable with a conventional radar. In most SAR applications, a single radiating element is translated along a trajectory, to take up sequential sampling positions. At each of these sampling points, a signal is transmitted and the amplitude and the phase of the radar signals received in response to that transmission are stored. After the radiating element has traversed a distance substantially equivalent to the length of the synthetic array, the signals in storage are somewhat similar to the signals that would have been received by the elements of an actual linear array antenna.
A SAR can obtain a resolution similar to a conventional linear array of equivalent length as a consequence of the coherent transmission from the sampling points of the SAR. The stored SAR signals are subjected to an operation which corresponds to that used in forming the effective antenna pattern of a physical linear array. That is, the signals are added vectorially, so that the resulting output of the SAR is substantially the same as could be achieved with the use of a physically long, linear antenna array.
In generating the synthetic antenna, the signal processing equipment of an SAR operates on a basic assumption that the radar platform travels along a straight line trajectory at a constant speed. In practice, an aircraft carrying the radar antenna is subject to deviations from such non-accelerated flight. It is therefore necessary to provide compensation for these perturbations to straight-line motion. This motion compensation must be capable of detecting the deviation of the radar platform path from a true linear path.
Briefly, and referring now to FIG. 1 in the drawings, an SAR system carried by an aircraft 10 maps a target region 12 by transmitting and receiving radar signals at various sampling points S1, . . . SN, along the flight path 14 of the aircraft. In this regard, the SAR system may be positioned in the nose portion 15 of the aircraft. As the SAR system operates, errors can be introduced into the system that, if not compensated for, will corrupt the signal phase, possibly to the extent that the resulting degraded image is of no practical use. Such errors can be introduced from a variety of sources, including errors in motion measurements, inaccurate acceleration estimates and atmospheric/ionospheric propagation effects. Such errors can be rather arbitrary and perhaps describable by a wide-band random process. A typical requirement of a SAR system is the phase errors must be corrected with an accuracy of about 10 degrees root mean square error (RMSE) or better (e.g., 7 degrees) so that the quality of the resulting SAR image is not compromised. Thus, a need exists to process the received radar signals to compensate for such errors to achieve the highest quality SAR image. Conventional processing techniques, however, typically suffer from lack of accuracy in situations where target/clutter-to-noise ratios are low or there are several competing scatterers in a given range cell. Such drawbacks are typical, for example, in techniques based on phase (pulse-pair product) comparisons.
In light of the foregoing background, the present invention provides an improved system, method and computer program product for reducing errors in synthetic aperture radar (SAR) signals. The system, method and computer program product of embodiments of the present invention implement maximum likelihood estimation for autofocusing SAR signals to reduce errors in SAR signals, particularly at low signal/clutter-to-noise ratios and in situations where multiple scatterers are present in the same range line. Advantageously, the system, method and computer program product use superresolution processing along the slow-time, or azimuth, positions to separate closely spaced scatterers on the same range lines and estimate the signal plus clutter components with higher fidelity.
According to one aspect of the present invention, a system is provided for reducing errors in synthetic aperture radar signals from a plurality of range lines where each range line includes a plurality of azimuth positions. The system comprises an autofocus processor capable of receiving a plurality of slow-time samples representing radar signals for a plurality of azimuth positions for a plurality of range lines. The autofocus processor is also capable of estimating a phase error for each slow-time sample and thereafter compensating the plurality of slow-time samples by the estimated phase errors to obtain a plurality of range-line samples. For example, the autofocus processor can compensate the plurality of slow-time samples based upon a diagonal random phasor matrix. More particularly, the autofocus processor can compensate the plurality of slow-time samples by multiplying the slow-time samples {right arrow over (x)}m by a complex conjugate of the diagonal random phasor matrix to obtain a plurality of range-line samples, {right arrow over (y)}m. In this regard, {right arrow over (x)}m represents a plurality of slow-time samples for each range line m, and {right arrow over (y)}m represents a plurality of range-line samples for each range line.
With the range-line samples, the autofocus processor is capable of processing the range-line samples according to a superresolution signal processing technique to thereby obtain a plurality of Doppler frequencies for a plurality of point scatterers at each range line. In this regard, the autofocus processor can process the range-line samples according to a superresolution signal processing technique including Constrained Total Least Squares parameter estimation. With the Doppler frequencies, then, the autofocus processor can reconstruct a true signal for each range line based upon the plurality of Doppler frequencies and thereafter obtain a correction to the estimated phase error for each slow-time sample based upon the range-line samples and the true signals.
The autofocus processor can be capable of reconstructing a true signal based upon a plurality of Doppler frequency steering matrices, Êm. In this regard, the plurality of Doppler frequency steering matrices can be represented as follows:
Êm=E({circumflex over (f)}1,m, . . . , {circumflex over (f)}K,m),
where {circumflex over (f)}k,m represents the Doppler frequency for each of K point scatterers at each range line m. The autofocus processor can then reconstruct a true signal  for each range line according to the following:
=Êm,
where  represents a plurality of complex amplitudes of the scatterers at each range line. Further, the autofocus processor can be capable of determining the plurality of complex amplitudes of the scatterers at each range line according to the following:
=(Êm*Êm)xe2x88x92Êm*{right arrow over (y)}m.
More particularly, then, the autofocus processor can be capable of obtaining a correction xcex4{circumflex over (xcfx86)}n to the estimated phase error for each slow-time sample according to the following:       δ    ⁢                  φ        ^            n        =      arg    ⁢                  {                              ∑            m                    ⁢                                    y                              n                ,                m                                      ⁢                                          s                                  ^                  -                                                            n                ,                m                                                    }            .      
In obtaining the correction, n=xe2x88x92N, . . . 0, . . . N represents each of 2N+1 slow-time samples at each range line.
To further reduce errors in the radar signals, the autofocus processor can also be capable of replacing the slow-time samples with the range-line samples when a difference between the estimated phase error for each slow-time sample and a respective correction is greater than a predetermined threshold. Then, the autofocus processor can compensate the slow-time samples, process the range-line samples, reconstruct the true signal, obtain the correction, and replace the slow-time samples until a root mean square error (RMSE) of the estimated phase correction for each slow-time is less than the predetermined threshold, typically after a number of iterations of the method.
According to another aspect of the present invention, a system is provided for determining an accuracy of estimated phase errors in synthetic aperture radar signals, where the signals are from a plurality of range lines that each includes a plurality of azimuth positions. The system includes a processing element capable of calculating true signals for a plurality of slow-time samples for the plurality of range lines. The processing element can be capable of selecting a plurality of signal scatterer parameters. In such an instance, processing element can calculate the true signals based upon the point scatterer parameters. Alternatively, the processing element can calculate the true signals by first receiving the plurality of slow-time samples and thereafter estimating a phase error for each slow-time sample. Then, the processing element can compensate the plurality of slow-time samples by the estimated phase errors to obtain a plurality of range-line samples. The processing element next processes the range-line samples according to a superresolution signal processing technique to thereby obtain a plurality of Doppler frequencies for a plurality of point scatterers at each range line. And then the processing element reconstructs a true signal for each range line based upon the plurality of Doppler frequencies.
In addition to calculating the true signals, the processing element is also capable of determining a true signal power for each slow-time sample summed over the plurality of range lines and a total true signal power, where the true signal powers are based upon the true signals and the total true signal power is based upon amplitudes of the scatterers. Additionally, the processing element can determine a Cramer Rao Bound (CRB) based upon a clutter-plus-receiver noise power, the true signal powers, a dominant scatterer power, the number of slow time samples and the total true signal power. In this regard, processing element can also be capable of estimating the clutter-plus-receiver noise power upon a uniform clutter noise and a receiver noise model. Based upon the CRB, then, the processing element can determine a root mean square error. A method and computer program product for reducing errors, and a method and computer program product for determining an accuracy of estimated phase errors are also provided.